Problem: Solve for $x$ and $y$ using elimination. ${x+3y = 24}$ ${-x+5y = 16}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $8y = 40$ $\dfrac{8y}{{8}} = \dfrac{40}{{8}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {x+3y = 24}\thinspace$ to find $x$ ${x + 3}{(5)}{= 24}$ $x+15 = 24$ $x+15{-15} = 24{-15}$ ${x = 9}$ You can also plug ${y = 5}$ into $\thinspace {-x+5y = 16}\thinspace$ and get the same answer for $x$ : ${-x + 5}{(5)}{= 16}$ ${x = 9}$